The following analysis focuses on spell scrolls in particular, but the same logic applies to spellbooks. In terms of their effect on the number of spells in your spellbook, the two are interchangeable.
In my experience, you won't be a burden
I play a wizard in a game where due to some unfortunate relations with the town militia, my adventuring party and I aren't welcome in town any more. Long story short, me and my DM agreed that since I wouldn't have any access to the components I would need to copy spells into my spellbook in the wilderness, I can't copy over any scrolls into my spellbook for the moment.
I've spent a few levels in this situation (4th to 7th) and it really hasn't been that much of an issue. I feel like I still have plenty of options and never found myself in a situation where I couldn't contribute in some meaningful way.
Granted that's just my personal experience. So let me dive into a few clues in the game's structure that tell us that wizards don't need to get scrolls to be successful.
Even without scrolls, wizards get a huge spell selection.
Wizards start with 6 spells at 1st level, and then gain 2 every level thereafter. Assuming you went pure wizard, by 20th level you will have an absolute minimum of 44 spells in your spellbook that you can prepare from every day. Compare that to other arcane casters: Sorcerers and Warlocks have at most 15 spells known at any given time, Bards have 22 (or 24 if you take the college of lore). And all of those classes start with a fewer number of spells known than you have in your book at 1st level. All of this leads to one conclusion:
By design, wizards have access to more spells than any other arcane class. Only divine spellcasters who can prepare spells off of their entire spell list (clerics, druids, and paladins) can compete in terms of spells available at any given moment.
Spell scrolls are magic items
Magic items, including spell scrolls, are defined in the DMG and the Dungeon Master is given free reign on how much treasure to give out to the party. Under this design, the game has to be balanced in such a way that even without magic items, characters can be successful (since the DM could elect not to give out any magic items at all).
Since spell scrolls are a magic item, and their availability is at the DM's discretion, we can then conclude that the design of the wizard was crafted such that they do not need scrolls to be successful and impactful in the game.